Vehicle suspensions which employ pneumatic springs, such as airsprings, as the load-supporting elements are widely used on modern heavy-duty highway trucks and trailers. In addition to being relatively light compared to other types of springs, the stiffness of an airspring varies nearly in proportion to the load being carried. Hence, the natural frequency of an air suspension varies little with changes in load, allowing the suspension to provide a soft ride under a wide range of loads. Airsprings also permit the static height of the suspension to be maintained, independent of the load, through the use of a height control valve. The height control valve senses the position of the suspension and supplies or exhausts air from the airspring as required to maintain a constant ride height. These are particularly desirable features for large trucks since the load supported by the suspension can change significantly between the/fully loaded and lightly loaded conditions.
One characteristic of airsprings is that they have little inherent damping. As a result, suspensions which employ them are normally equipped with secondary damping devices, such as hydraulic "shock absorbers."
FIG. 1 is a schematic representation of a typical motor vehicle suspension system 10. A so-called "quarter-car" representation is shown corresponding to the suspension elements associated with one end of an axle 11. The vehicle body 12 is normally supported by a suspension spring 14 interposed in some manner between the axle and the body. A suspension damper 16, usually a hydraulic shock absorber, is also interposed between the axle and the body. Likewise, the axle is supported by the tire 18, which in effect is a spring 20 and a damper 22. The various linkages and attachments which locate these components are not relevant to the ensuing discussion and therefore are not shown.
The system 10 represented in FIG. 1 is a two-degree-of-freedom system since it has two discrete masses (the body 12 and axle 11) and therefore two natural frequencies (modes) of vibration. The lower frequency is referred to as the suspension bounce frequency and is characterized by the in-phase movement of the body 12 and the axle 11. For the stiffnesses and masses typical to cars and trucks, the bounce frequency is largely governed by the body mass and the suspension spring stiffness, the axle mass and tire stiffness having relatively little influence. The motion of the body mass at the bounce frequency is normally large compared to that of the axle.
In order to best provide for human comfort, it is desirable for the suspension spring to have a low bounce natural frequency. A suspension bounce frequency of one cycle per second (Hz) is often considered ideal in this regard. Actual suspensions often have higher bounce natural frequencies, dictated by the need to have sufficient spring stiffness to limit the change in vehicle height or attitude when the vehicle load changes, or to limit body pitch under braking and acceleration forces.
The second natural frequency is referred to as the axle-hop frequency and is characterized by the out-of-phase motion of the axle 11 with respect to the body 12. The axle-hop frequency is normally much higher than the bounce frequency, typically falling in the 10 to 12 Hz range for most modern cars and trucks. The amplitude of the axle motion will be large compared to that of the body at this resonant frequency. The axle-hop frequency is mostly a function of the tire stiffness, suspension stiffness, and axle mass and is influenced much less by the body mass.
A primary objective of a suspension system is to minimize the transmission of road disturbances to the vehicle chassis and its occupants The role of damping is essential in achieving this objective.
FIG. 2 shows the frequency response for a suspension having a bounce frequency of around 1.5 Hz and an axle-hop frequency near 10 Hz for two different levels of damping. The curves represent the transmissibility of the suspension, i.e., the ratio of the response amplitude of the body 12 to the input amplitude at the tire 18. A transmissibility greater than one indicates the input motion is amplified; less than one indicates attenuation. While increased damping provides reduced transmissibility of inputs at the two natural frequencies, it also results in poorer isolation of the body at intermediate frequencies and frequencies above the axle-hop frequency Good suspension isolation in the range of 5 to 9 Hz is particularly important for large highway trucks since such trucks typically have a frame flexure mode in that vicinity that is easily excited by road inputs and tire non-uniformities.
The foregoing discussion and principles are known to those skilled in the art of suspension design and vehicle dynamics. It is illustrative of the fact that damping is required primarily to control motion at the suspension's resonant frequencies, but is otherwise detrimental to ride performance.
Shock absorbers are not frequency-dependent devices. The force generated by a shock absorber is normally a function only of its piston velocity. The valving may be tailored to provide nearly linear performance or highly non-linear force vs. velocity characteristics, but the damping force generated at one frequency will be the same as is generated at another frequency given the same imposed velocity.
It would be advantageous to have a damping means that is frequency-dependent, that is, one which would provide a large amount of damping at the suspension's two resonant frequencies, thus attenuating the amplification of motion at those frequencies, but which would provide relatively little damping at other frequencies.
The amount of damping in a system is normally expressed in terms of a given fraction of critical damping. Critical damping is the minimum amount of damping needed to make the transient response of a spring/mass system non-oscillatory. Critical damping for a simple spring/mass system is given by: ##EQU1## where k is the spring rate and m is the mass.
Most automotive suspensions have dampers which provide some fraction of critical damping which the designer feels provides the best ride qualities. Twenty to thirty percent of critical damping is typical.
The critical damping for a system varies with the square root of both the mass and the spring stiffness. In many vehicles, such as automobiles, the range of loading is relatively small. The mass carried by the suspension might increase by, at most, 40% between a lightly loaded and a fully loaded condition. The springs, which are usually steel leaf or helical coil, also have a nearly constant spring rate. So, the amount of damping required to maintain a fixed percentage of critical damping max, only vary by 18% or so. Consequently, this type of vehicle generally does not need adjustable dampers to provide satisfactory ride performance over its normal range of loading.
A large highway tractor with an air suspension is a quite different situation. The load on the tractor's tandem suspension with an empty trailer is only about one-third the load in the fully laden condition. If the tractor is bobtail (no trailer), the load may only be one-tenth of the full load. In addition, the spring rate of an air suspension is approximately proportional to the load being supported, so k in Equation 1 changes with load as well as does m. Thus, if the load changes by a factor of three, the critical damping for the system also changes by a factor of three. If the suspension dampers are sized for the fully loaded condition, then the suspension will have too much damping when lightly loaded and a harsh ride will result. Conversely, if the dampers are sized for good ride quality in the light condition, they will not provide sufficient control under heavy loads. Therefore, it would be very desirable to have the damping on truck air suspensions be load-dependent.
The basic concept of a pneumatically damped airspring is illustrated in FIG. 3. An airspring 24 of constant effective area is represented by a piston 26 supported by pressurized air 28 contained within a cylinder 30. A conduit 32 connects the air volume in the spring to a secondary air chamber 34. The airspring 24 supports a single mass 36.
The spring rate of a constant area airspring is given by the relation: ##EQU2## where
A=the piston area
p=the absolute air pressure
v=the air volume
n=the polytropic gas constant.
If the conduit is very large, so that air may flow freely between the spring and secondary air chamber, then the effective air volume is essentially the total of the spring and chamber volumes. Since the spring rate is inversely proportional to the spring volume, this yields a relatively low spring rate. The frequency response of the system with a very large conduit 32 is indicated by curve B in FIG. 4
On the other hand, if the conduit is very small, so that little air may pass between the spring and the secondary chamber, the effective volume will be essentially that of the spring alone. The response of this system with a very small conduit 32 is indicated by curve A in FIG. 4. The higher natural frequency reflects the higher spring rate due to the smaller effective air volume. As with the large conduit, the response is essentially undamped.
If the conduit 32 is sized appropriately, however, the response shown in curve C of FIG. 4 can be achieved. The effective volume of the spring lies somewhere between the two extremes indicated by curves A and B and results in an intermediate natural frequency. In addition, the system now exhibits a certain amount of damping.
The damping is the result of pumping energy losses in the conduit 32. If the conduit is too small, the air flow rate is insufficient to generate significant energy loss. Conversely, if the conduit is too large, the pressure drop across it is too small to generate significant energy loss. The diameter and length of the conduit will determine the frequency at which peak damping occurs, while the volume of the secondary chamber 34 generally governs how much damping can be achieved. The larger the secondary volume, the greater the damping that can be achieved. A larger volume tends to maintain a larger pressure differential between the airspring and the reservoir as the airspring 24 cycles.
While conceptually simple, the gas dynamics of air damping are complex. The problem does not lend itself readily to analytical treatment, and tuning of an air damping circuit is best accomplished through empirical methods.
An important characteristic of the system of FIG. 3 is that the energy dissipation is a function of frequency. For a given level of damping at resonance, a pneumatically-damped airspring will have high-frequency isolation performance superior to that of a linear viscously damped system, since it provides reduced damping off-resonance where damping degrades isolation performance.
A second characteristic of the system of FIG. 3 is that the amount of damping generated varies with the nominal pressure in the system. For a given displacement of the mass, the pressure differential across the conduit will increase as the system pressure increases. The higher pressure drop results in greater pumping losses and hence, increased damping. Since the pressure in the airspring is proportional to the load being supported, the damping therefore tends to be load-dependent.
The system of FIG. 3 is a single degree of freedom system with only one natural frequency and is not an appropriate solution for a vehicle suspension where there are two resonant frequencies to control. If the system is tuned for the, suspension bounce frequency, then almost no damping is provided at the axle-hop frequency. Likewise, if the system is tuned for axle-hop control, too little damping exists at the bounce frequency.